Problem: Multiply the following complex numbers: $({-3-2i}) \cdot ({-4-i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3-2i}) \cdot ({-4-i}) = $ $ ({-3} \cdot {-4}) + ({-3} \cdot {-1}i) + ({-2}i \cdot {-4}) + ({-2}i \cdot {-1}i) $ Then simplify the terms: $ (12) + (3i) + (8i) + (2 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 12 + (3 + 8)i + 2i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 12 + (3 + 8)i - 2 $ The result is simplified: $ (12 - 2) + (11i) = 10+11i $